What is the ruling on paying an amount as a down payment for a relative's car, provided that the amount is paid in monthly installments, and the remainder of his earnings is divided equally, and if the car is sold, the down payment is recovered and the sale price is divided equally? And what is the ruling on registering the car in the relative's name?

The described transaction is not valid, neither as a Mudarabah (profit-sharing partnership) nor as a Sharikah (general partnership).

As for Mudarabah, it is because it is an exclusive trade, and its contract is not valid for specific works such as tailoring or baking. Rather, it is for seeking profit through buying and selling, and the work within it is not restricted.

As for Sharikah, it is because one of the conditions for a valid partnership in assets is that the capital be present and not a debt. In this transaction, the questioner's relative does not have present money; rather, he will work to repay. The fact that the questioner will recover his capital upon annulment and share with his relative in the remainder, in addition to sharing in the profits before that, is outside the norms of both Mudarabah and Sharikah.

Instead, the questioner can lend money to his relative, or he can partner with him in an undivided share of the car, or he can make his participation a diminishing partnership.